Linked List Random Node

Given a singly linked list, return a random node's value from the linked list. Each node must have thesame probability of being chosen.

Follow up:

What if the linked list is extremely large and its length is unknown to you? Could you solve this efficiently without using extra space?

Example:

// Init a singly linked list [1,2,3].
ListNode head = new ListNode(1);
head.next = new ListNode(2);
head.next.next = new ListNode(3);
Solution solution = new Solution(head);

// getRandom() should return either 1, 2, or 3 randomly. Each element should have equal probability of returning.
solution.getRandom();

思路：用hashmap来存node，和index，然后用随机函数来取。

/**
* Definition for singly-linked list.
* public class ListNode {
*     int val;
*     ListNode next;
*     ListNode(int x) { val = x; }
* }
*/
public class Solution {

/** @param head The linked list's head.
Note that the head is guaranteed to be not null, so it contains at least one node. */
HashMap<Integer, ListNode> hashmap = new HashMap<Integer, ListNode>();
private int length = 0;
public Solution(ListNode head) {
ListNode node = head;
int index = 1;
while(node!=null){
length++;
hashmap.put(index, node);
node = node.next;
index++;
}
}

/** Returns a random node's value. */
public int getRandom() {
int value = (int)(Math.random()*length)+1;
return hashmap.get(value).val;
}
}

/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(head);
* int param_1 = obj.getRandom();
*/

Follow up question: 实际上就是水塘采样。算法就是随时get当前的长度，取random [0,n)，如果取到0就取当前刚进来的node，如果不是，那就取之前那个random的值，这样能保证每个点都是随机的。证明过程，有个状态图。



/**
* Definition for singly-linked list.
* public class ListNode {
* int val;
* ListNode next;
* ListNode(int x) { val = x; }
* }
*/
public class Solution {

/** @param head The linked list's head.
Note that the head is guaranteed to be not null, so it contains at least one node. */
private ListNode curNode = null;
private ListNode preNode = null;
private ListNode beginNode = null;
public Solution(ListNode head) {
beginNode = head;
}

/** Returns a random node's value. */
public int getRandom() {
preNode = beginNode;
curNode = beginNode;
int count = 1;
while(curNode != null) {
int randValue = (int)(Math.random()*count);
if(randValue == 0){
preNode = curNode;
}
curNode = curNode.next;
count++;
}

return preNode.val;
}
}

/**
* Your Solution object will be instantiated and called as such:
* Solution obj = new Solution(head);
* int param_1 = obj.getRandom();
*/